Recall that a covariant 4-vector is obtained from a contravariant one by changing the sign of the

Question:

Recall that a covariant 4-vector is obtained from a contravariant one by changing the sign of the zeroth component. The same goes for tensors: When you "lower an index" to make it covariant, you change the sign if that index is zero. Compute the tensor invariants Fμv Fμv, Gμv Gμv, and Fμv Vμv, in terms of E and B. Compare Prob. 12.46.